SHEAR DEFORMABLE BEAMS ON NONLINEAR VISCOELASTIC FOUNDATION UNDER MOVING LOADING

In this paper, a boundary element method is developed for the nonlinear response of shear deformable beams of simply or multiply connected constant cross section, traversed by moving loads, resting on tensionless nonlinear viscoelastic foundation, undergoing moderate large deflections under general boundary conditions. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse moving loading as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Three boundary value problems are formulated with respect to the transverse displacement, to the axial displacement and to a stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a system of nonlinear differential algebraic equations (DAE), which is solved using an efficient time discretization scheme, from which the transverse and axial displacements are computed. The evaluation of the shear deformation coefficient is accomplished from the aforementioned stress function using only boundary integration. Analyses are performed to investigate the effects of various parameters, such as the load velocity, load frequency, shear rigidity, foundation nonlinearity, damping, on the beam displacements and stress resultants and to examine how the consideration of shear and axial compression affect the response of the system.